1. Field of the Invention
The present invention relates to the sphere of petroleum reservoir exploration and development. More particularly, the invention relates to the evaluation of such reservoirs through the study and the optimization of production schemes for such petroleum reservoirs.
2. Description of the Prior Art
A production scheme is a reservoir development option. It combines all the parameters required for bringing a reservoir on stream. These parameters can be the position of a well, the completion level, the drilling technique, etc.
A reservoir survey comprises two main stages: a reservoir characterization stage and a production forecast stage.
The reservoir characterization stage constructs a reservoir model. A reservoir model is a model describing the spatial structure of the reservoir in a form of a space discretization which is materialized by a set of grid cells. Property values characterizing the reservoir: porosity, permeability, lithology, pressure, nature of the fluids, etc., are associated with each cell. Engineers only have access to a tiny part of the reservoir under study (measurements on cores, logs, well tests, etc.). They have to extrapolate these punctual data over the entire oil field to construct a reliable reservoir model. The notion of uncertainty therefore constantly has to be taken into account.
A “flow simulator” is used for production forecasting to enhance the production or, in general, to increase the commercial efficiency of the field, A flow simulator is software allowing, among other things, modelling of the production of a reservoir as a function of time from measurements describing the reservoir, that is from the reservoir model.
A flow simulator operates by accepting input parameters and by solving physical equations of fluid mechanics in porous media, in order to deliver information referred to as responses. All of the input parameters are contained in the reservoir model. The properties associated with the cells of this model are then referred to as parameters. These parameters are notably associated with the reservoir geology, the petrophysical properties, the reservoir development and the numerical options of the simulator. The responses (output data) supplied by the simulator are, for example, the oil, water or gas production of the reservoir and of each well for different times. Generally, for each value of the various input parameters, the flow simulator sends a single value for each response (output). The flow simulator is then referred to as deterministic.
However, the majority of the input parameters are uncertain. The effect of these uncertainties is that it is not possible to assign a single value having certainty to a parameter of the reservoir model. For example, the porosity at one point of the reservoir of 20% cannot be assured. It can be considered that the porosity ranges between 15% and 25% at this point. This is notably due to the fact that the input parameters are determined by means of a limited number of measurements and data. The possible responses of the flow simulator are therefore multiple, considering the uncertainty inherent in the reservoir model. In the above example, there will be a response from the simulator if the porosity is 15%, a different response if the porosity is 20.5%, etc. It is therefore essential to be able to quantify the uncertainty on the simulator output data. Similarly, correct characterization of the uncertainty of the input parameters is also essential. It is also important to determine the input parameters that have a significant effect on the responses of interest.
Oil reservoir development specialists therefore have to integrate these uncertainty notions into the evaluation of a reservoir to determine, for example, optimum production conditions.
In order to properly characterize the impact of each uncertainty on the oil production, many production scenarios have to be tested and a large number of reservoir simulations are therefore necessary.
However, in the petroleum industry, in order to be more and more reliable and predictive, the trend is to increasingly use complex flow simulators requiring a more and more detailed (several million grid cells) reservoir model. But, considering the considerable time required to carry out a flow simulation, it is unthinkable to test all the possible scenarios via a flow simulator.
In order to avoid carrying out a large number of simulations, a technique described in French Patent 2,874,706, based on designed experiments, is used. This method allows managing uncertainties via the construction of approximate models, referred to as “response surfaces”, obtained by kriging for example. These surfaces provide responses that are approximate to those from the flow simulator.
However, any response surface makes a more or less significant prediction error, depending on the response to be approximated. In general, addition of information (that is simulations) allows constructing a more and more predictive response surface.